After the European Central Bank announced an aggressive plan to deal with the eurozone debt crisis, U.S. stocks started climbing, and climbing some more. The Dow Jones industrial average ended the day up 245 points at 13,292, the highest close since before the Great Recession began in late 2007.

The euphoria on Wall Street grew out of events in Germany, where the ECB said it would continue to hold down interest rates and launch a program to buy European government bonds. Stocks in European and U.S. markets took off.

The reaction reflected relief. Investors now are more hopeful that European officials can hammer out a permanent solution to the complicated debt troubles that have been weighing down their governments.

Crouch said events in Europe are important to U.S. investors because any banking crisis over there could roil financial markets here.

"Ever since we went to a global economy, there really is no separation in terms of national borders," he said. "The world financial markets are inextricably linked."

But investors should hold on to their hats; this month's ride could turn bumpy at any moment. In fact, Friday morning could bring a new jolt when the U.S. Labor Department releases its monthly unemployment report at 8:30.

Most economists have been predicting that employers added just 125,000 jobs in August and that the unemployment rate held at about July's 8.3 percent level.

But those forecasts could turn out to be wrong. Thursday actually brought some signs there could be a surprise on the upside. Payroll processor ADP said private employers added 201,000 jobs in August, and outplacement firm Challenger, Gray & Christmas said layoffs hit a 20-month low last month. Those two new indicators could signal a stronger-than-expected jobs report on Friday.

Here's where things really get weird. If the jobs report were to come in really strong, say, 250,000 jobs, it might discourage policymakers at the Federal Reserve from doing more to stimulate growth. Many stock investors would be disappointed if Fed officials were to take stimulus off the table. That disappointment could actually hurt the stock market.

In any case, the Fed's intentions will be revealed when policymakers hold a meeting Tuesday and Wednesday to vote on what to do next. And back in Europe, a German court is expected to issue a key ruling on the constitutionality of debt-bailout actions.

With such big uncertainties hanging above, some Wall Street analysts say they would not be surprised if the stock market would see a downward "correction" of as much as 10 percent in coming weeks.

Those very gloomy predictions may be colored by September's bad reputation. Analysts refer to the "September effect," noting that over the past four decades, September has come in as the worst month for stock performance.

It was especially bad in the presidential election cycle of 2008. The Dow took some terrifying drops that September, ending the month down 6 percent. That October was brutal too as the global financial crisis deepened.

But Nariman Behravesh, chief economist for IHS Global Insight, a forecasting firm, said that September isn't always a tough month. In fact, in September 2010, the stock market shot up.

Assuming Europe can indeed avoid an implosion, this autumn may actually turn out to be a balmy period, at least in terms of the economy. "Profits are still decent and a lot of companies are making good money," Behravesh said. "The United States is still a safe haven."